Issue 3141

core/src/main/scala/cats/Foldable.scala

@@ -394,6 +394,26 @@ import Foldable.sentinel
     }
   }
 
+  /**
+   * Fold implemented using the given `Applicative[G]` and `Monoid[A]` instance.
+   *
+   * This method is identical to fold, except that we use `Applicative[G]` and `Monoid[A]`
+   * to combine a's inside an applicative G.
+   *
+   * For example:
+   *
+   * {{{
+   * scala> import cats.implicits._
+   * scala> val F = Foldable[List]
+   * scala> F.foldA(List(Either.right[String, Int](1), Either.right[String, Int](2)))
+   * res0: Either[String, Int] = Right(3)
+   * }}}
+   *
+   * `noop` usage description [[https://github.com/typelevel/simulacrum/issues/162 here]]
+   */
+  @noop def foldA[G[_], A](fga: F[G[A]])(implicit G: Applicative[G], A: Monoid[A]): G[A] =
+    fold(fga)(Applicative.monoid)
+
   /**
    * Fold implemented by mapping `A` values into `B` in a context `G` and then
    * combining them using the `MonoidK[G]` instance.

core/src/main/scala/cats/Reducible.scala

@@ -82,6 +82,22 @@ import simulacrum.{noop, typeclass}
   def reduceLeftM[G[_], A, B](fa: F[A])(f: A => G[B])(g: (B, A) => G[B])(implicit G: FlatMap[G]): G[B] =
     reduceLeftTo(fa)(f)((gb, a) => G.flatMap(gb)(g(_, a)))
 
+  /**
+   * Reduce a `F[G[A]]` value using `Applicative[G]` and `Semigroup[A]`, a universal
+   * semigroup for `G[_]`.
+   *
+   * `noop` usage description [[https://github.com/typelevel/simulacrum/issues/162 here]]
+   */
+  @noop def reduceA[G[_], A](fga: F[G[A]])(implicit G: Apply[G], A: Semigroup[A]): G[A] =
+    reduce(fga)(Apply.semigroup)
+
+  /**
+   * Apply `f` to each `a` of `fa` and combine the result into Apply[G] using the
+   * given `Semigroup[B]`.
+   */
+  def reduceMapA[G[_], A, B](fa: F[A])(f: A => G[B])(implicit G: Apply[G], B: Semigroup[B]): G[B] =
+    reduceLeftTo(fa)(f)((gb, a) => G.map2(gb, f(a))(B.combine))
+
   /**
    * Monadic reducing by mapping the `A` values to `G[B]`. combining
    * the `B` values using the given `Semigroup[B]` instance.

core/src/main/scala/cats/syntax/foldable.scala

@@ -46,6 +46,9 @@ final class FoldableOps[F[_], A](private val fa: F[A]) extends AnyVal {
   def foldr[B](b: Eval[B])(f: (A, Eval[B]) => Eval[B])(implicit F: Foldable[F]): Eval[B] =
     F.foldRight(fa, b)(f)
 
+  def foldA[G[_], B](implicit F: Foldable[F], ev: A <:< G[B], G: Applicative[G], B: Monoid[B]): G[B] =
+    F.foldA[G, B](fa.asInstanceOf[F[G[B]]])
+
   /**
    * test if `F[A]` contains an `A`, named contains_ to avoid conflict with existing contains which uses universal equality
    *

core/src/main/scala/cats/syntax/reducible.scala

@@ -29,5 +29,9 @@ final class ReducibleOps0[F[_], A](private val fa: F[A]) extends AnyVal {
    * a: String = "foo321"
    * }}}
    * */
-  def reduceMapK[G[_], B](f: A => G[B])(implicit F: Reducible[F], G: SemigroupK[G]): G[B] = F.reduceMapK[G, A, B](fa)(f)
+  def reduceMapK[G[_], B](f: A => G[B])(implicit F: Reducible[F], G: SemigroupK[G]): G[B] =
+    F.reduceLeftTo(fa)(f)((b, a) => G.combineK(b, f(a)))
+
+  def reduceA[G[_], B](implicit F: Reducible[F], ev: A <:< G[B], G: Apply[G], B: Semigroup[B]): G[B] =
+    F.reduceA[G, B](fa.asInstanceOf[F[G[B]]])
 }

tests/src/test/scala-2.12/cats/tests/NonEmptyStreamSuite.scala

@@ -166,4 +166,7 @@ class ReducibleNonEmptyStreamSuite extends ReducibleSuite[NonEmptyStream]("NonEm
     val tailStart: Long = start + 1L
     NonEmptyStream(start, tailStart.to(endInclusive).toStream)
   }
+
+  def rangeE[L, R](el: Either[L, R], els: Either[L, R]*): NonEmptyStream[Either[L, R]] =
+    NonEmptyStream(el, els: _*)
 }

tests/src/test/scala-2.13+/cats/tests/NonEmptyLazyListSuite.scala

@@ -137,4 +137,7 @@ class ReducibleNonEmptyLazyListSuite extends ReducibleSuite[NonEmptyLazyList]("N
 
   def range(start: Long, endInclusive: Long): NonEmptyLazyList[Long] =
     NonEmptyLazyList(start, (start + 1L).to(endInclusive): _*)
+
+  def rangeE[L, R](el: Either[L, R], els: Either[L, R]*): NonEmptyLazyList[Either[L, R]] =
+    NonEmptyLazyList(el, els: _*)
 }

tests/src/test/scala/cats/tests/FoldableSuite.scala

@@ -456,6 +456,20 @@ class FoldableSuiteAdditional extends CatsSuite with ScalaVersionSpecificFoldabl
       Foldable[Stream].foldRight(fa, lb)(f)
   }
 
+  test(".foldA successful case") {
+    implicit val F = foldableStreamWithDefaultImpl
+    val ns = Stream.apply[Either[String, Int]](1.asRight, 2.asRight, 7.asRight)
+
+    assert(F.foldA(ns) == 10.asRight[String])
+  }
+
+  test(".foldA failed case") {
+    implicit val F = foldableStreamWithDefaultImpl
+    val ns = Stream.apply[Either[String, Int]](1.asRight, "boom!!!".asLeft, 7.asRight)
+
+    assert(ns.foldA == "boom!!!".asLeft[Int])
+  }
+
   test(".foldLeftM short-circuiting") {
     implicit val F = foldableStreamWithDefaultImpl
     val ns = Stream.continually(1)

tests/src/test/scala/cats/tests/NonEmptyChainSuite.scala

@@ -161,4 +161,7 @@ class ReducibleNonEmptyChainSuite extends ReducibleSuite[NonEmptyChain]("NonEmpt
 
   def range(start: Long, endInclusive: Long): NonEmptyChain[Long] =
     NonEmptyChain(start, (start + 1L).to(endInclusive): _*)
+
+  def rangeE[L, R](el: Either[L, R], els: Either[L, R]*): NonEmptyChain[Either[L, R]] =
+    NonEmptyChain(el, els: _*)
 }

tests/src/test/scala/cats/tests/NonEmptyListSuite.scala

@@ -370,4 +370,6 @@ class ReducibleNonEmptyListSuite extends ReducibleSuite[NonEmptyList]("NonEmptyL
     NonEmptyList(start, (tailStart).to(endInclusive).toList)
   }
 
+  def rangeE[L, R](el: Either[L, R], els: Either[L, R]*): NonEmptyList[Either[L, R]] =
+    NonEmptyList(el, List(els: _*))
 }

tests/src/test/scala/cats/tests/NonEmptyVectorSuite.scala

@@ -403,4 +403,7 @@ class ReducibleNonEmptyVectorSuite extends ReducibleSuite[NonEmptyVector]("NonEm
     val tailStart: Long = start + 1L
     NonEmptyVector(start, (tailStart).to(endInclusive).toVector)
   }
+
+  def rangeE[L, R](el: Either[L, R], els: Either[L, R]*): NonEmptyVector[Either[L, R]] =
+    NonEmptyVector(el, Vector(els: _*))
 }

tests/src/test/scala/cats/tests/ReducibleSuite.scala

@@ -77,6 +77,7 @@ abstract class ReducibleSuite[F[_]: Reducible](name: String)(implicit ArbFInt: A
     extends FoldableSuite[F](name) {
 
   def range(start: Long, endInclusive: Long): F[Long]
+  def rangeE[L, R](el: Either[L, R], els: Either[L, R]*): F[Either[L, R]]
 
   test(s"Reducible[$name].reduceLeftM stack safety") {
     def nonzero(acc: Long, x: Long): Option[Long] =
@@ -88,6 +89,33 @@ abstract class ReducibleSuite[F[_]: Reducible](name: String)(implicit ArbFInt: A
     actual should ===(Some(expected))
   }
 
+  test(s"Reducible[$name].reduceA successful case") {
+    val expected = 6
+    val actual = rangeE(1.asRight[String], 2.asRight[String], 3.asRight[String]).reduceA
+    actual should ===(expected.asRight[String])
+  }
+
+  test(s"Reducible[$name].reduceA failure case") {
+    val expected = "boom!!!"
+    val actual = rangeE(1.asRight, "boom!!!".asLeft, 3.asRight).reduceA
+    actual should ===(expected.asLeft[Int])
+  }
+
+  test(s"Reducible[$name].reduceMapA successful case") {
+    val expected = "123"
+    val actual = range(1, 3).reduceMapA(_.toString.some)
+
+    actual should ===(expected.some)
+  }
+
+  test(s"Reducible[$name].reduceMapA failure case") {
+    def intToString(i: Long): Either[String, Int] = if (i == 2) i.toInt.asRight else "boom!!!".asLeft
+
+    val expected = "boom!!!"
+    val actual = range(1, 3).reduceMapA(intToString)
+    actual should ===(expected.asLeft[Int])
+  }
+
   test(s"Reducible[$name].toNonEmptyList/toList consistency") {
     forAll { fa: F[Int] =>
       fa.toList.toNel should ===(Some(fa.toNonEmptyList))